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3 years ago

There are nine cheerleaders how many different arrangements can the cheerleaders march one behind the other

Mathematics

1 answer:

babymother [125]3 years ago

3 0

<h3>Answer: 362,880</h3>

note: this is one single number. The comma helps make it more readable

=============================================

Explanation:

We have 9 positions to fill. The first position has 9 choices, the second has 8 (since we cannot pick the same person twice), then 7, then 6, and so on until we count down to 1. We multiply out all these values mentioned.

9*8*7*6*5*4*3*2*1 = 362,880

The idea of multiplying whole numbers counting down to 1 is a concept known as factorials. Because order matters, the value 362,880 represents the number of permutations possible.

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How do I solve -7 1/8 + 4 3/4

BabaBlast [244]

Answer:

Mixed fraction -2 3/8

decimal form -2.375

Improper fraction -19/8

Step-by-step explanation:

Convert the mixed numbers to improper fractions

then find the least common denminator and then combine them

so the answer is -19 / 8 or -2 3/8 as a mixed fraction

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3 years ago

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Step-by-step explanation:

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3 years ago

Complete the sequence of numbers in the set. Explain the pattern.

Firdavs [7]

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3 years ago

The following series are geometric series or a sum of two geometric series. Determine whether each series converges or not. For

Sergeeva-Olga [200]

Answer:

Required solution gives series (a) divergent, (b) convergent, (c) divergent.

Step-by-step explanation:

(a) Given,

$\sum_{n\to 0}^{\infty}\frac{2^n}{9^{2n}+1}$

To applying limit comparison test, let $a_n=\frac{2^n}{9^{2n}+1}$ and $b_n=\frac{9^{2n}}{2^n}$ . Then,

$\lim_{n\to\infty} \frac{a_n}{b_n}=\lim_{n\to\infty}(1+\frac{1}{9^{2n}})=1>0$

Because of the existance of limit and the series $\frac{9^{2n}}{2^n}$ is divergent since $\frac{9^{2n}}{2^n}=(\frac{9^2}{2})^n$ where $\frac{81}{2}>1$ , given series is divergent.

(b) Given,

$\sum_{n\to 1}^{\infty}(\frac{7^n}{7^n+4})$

Again to apply limit comparison test let $a_n=\frac{7^n}{7^n+4}$ and $b_n=\frac{1}{7^n}$ we get,

$\lim_{n\to \infty}\frac{a_n}{b_n}=\frac{1}{7^n+4}=0$

Since $\lim_{n\to \infty} \frac{1}{7^n}=0$ is convergent, by comparison test, given series is convergent.

$\sum_{n\to 1}^{\infty}\frac{5^n+2^n}{6^n}= \sum_{n\to 1}^{\infty}(\frac{5}{6})^n+\sum_{n\to 1}^{\infty}(\frac{1}{3})^n$ . Now applying Cauchy Root test on last two series, we will get,

\lim_{n\to \infty}|(\frac{5}{6})^n|^{\frac{1}{n}}=\frac{5}{6}=L_1
\lim_{n\to \infty}|(\frac{1}{3})^n|^{\frac{1}{n}}=\frac{1}{3}=L_2

Therefore,

$\lim_{n\to \infty}\frac{5^n+2^n}{6^n}=L_1+L_2=1.16>1$

Hence by Cauchy root test given series is divergent.

5 0

4 years ago